Algebra
Calculus
Trigonometry
Matrix
Question
Solve the quadratic equation
Solve by factoring
Solve using the quadratic formula
Solve by completing the square
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x1=−3,x2=2
Evaluate
(3x+1)2+(x+2)2=65
Expand the expression
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Evaluate
(3x+1)2+(x+2)2
Expand the expression
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Evaluate
(3x+1)2
Use (a+b)2=a2+2ab+b2 to expand the expression
(3x)2+2×3x×1+12
Calculate
9x2+6x+1
9x2+6x+1+(x+2)2
Expand the expression
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Evaluate
(x+2)2
Use (a+b)2=a2+2ab+b2 to expand the expression
x2+2x×2+22
Calculate
x2+4x+4
9x2+6x+1+x2+4x+4
Add the terms
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Evaluate
9x2+x2
Collect like terms by calculating the sum or difference of their coefficients
(9+1)x2
Add the numbers
10x2
10x2+6x+1+4x+4
Add the terms
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Evaluate
6x+4x
Collect like terms by calculating the sum or difference of their coefficients
(6+4)x
Add the numbers
10x
10x2+10x+1+4
Add the numbers
10x2+10x+5
10x2+10x+5=65
Move the expression to the left side
10x2+10x−60=0
Factor the expression
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Evaluate
10x2+10x−60
Rewrite the expression
10x2+10x−10×6
Factor out 10 from the expression
10(x2+x−6)
Factor the expression
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Evaluate
x2+x−6
Rewrite the expression
x2+(3−2)x−6
Calculate
x2+3x−2x−6
Rewrite the expression
x×x+x×3−2x−2×3
Factor out x from the expression
x(x+3)−2x−2×3
Factor out −2 from the expression
x(x+3)−2(x+3)
Factor out x+3 from the expression
(x−2)(x+3)
10(x−2)(x+3)
10(x−2)(x+3)=0
Divide the terms
(x−2)(x+3)=0
When the product of factors equals 0,at least one factor is 0
x−2=0x+3=0
Solve the equation for x
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Evaluate
x−2=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x=2x+3=0
Solve the equation for x
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Evaluate
x+3=0
Move the constant to the right-hand side and change its sign
x=0−3
Removing 0 doesn't change the value,so remove it from the expression
x=−3
x=2x=−3
Solution
x1=−3,x2=2
Show Solution
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